Permalink
Browse files

another comment

  • Loading branch information...
1 parent 2cc5a42 commit 4c2858d5eb822e71be546ab4d85d1a6c3f64e612 @AndrewDuncan AndrewDuncan committed Aug 19, 2011
Showing with 8 additions and 1 deletion.
  1. +8 −1 bass_serre_computability.tex
@@ -714,9 +714,16 @@ \section{Computability of Bass-Serre groups \label{bass-serre}}
sequence of the definition may not be immediately apparent.)}
\end{proof}
+\ajd{Before stating the next theorem the precise definition of \grz{n}-computable
+homomorphism and \grz{n}-decidable subgroup,
+should be given and discussed (see e.g. Cannonito\&Gatterdam '73).}
\begin{theorem} \label{fgoagogcomp}
-Suppose we have $G = \fgoagog$, where $\Gamma$ has $\nu$ vertices. Suppose all the $G_i$ are f.g. \grz{n}-computable groups for $n \geq 3$. Assume all the identified subgroups (\ajd{edge groups}) are \grz{n}-decidable, and all the isomorphisms $\phi_e$ are \grz{n}-computable. Then $G$ is \grz{n+1}-computable.
+Suppose we have $G = \fgoagog$, where $\Gamma$ has $\nu$ vertices. Suppose
+all the $G_i$ are f.g. \ajd{(``finitely generated'': weed out abbreviations)}
+\grz{n}-computable groups for $n \geq 3$. Assume all the identified subgroups
+(\ajd{edge groups}) are \grz{n}-decidable, and all the isomorphisms $\phi_e$
+are \grz{n}-computable. Then $G$ is \grz{n+1}-computable.
\end{theorem}
\begin{proof}

0 comments on commit 4c2858d

Please sign in to comment.